Harry's copy of Determine if vectors are perpendicular

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Harry Flynn

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Harry Flynn 7 years, 1 month ago

Created this as a copy of Determine if vectors are perpendicular.

Name	Status	Author	Last Modified
Determine if vectors are perpendicular	Has some problems	Newcastle University Mathematics and Statistics	20/11/2019 14:51
Vectors 2	draft	Violeta CIT	15/11/2017 14:58
Determine if vectors are perpendicular	draft	Adrian Jannetta	16/08/2023 14:56
Harry's copy of Determine if vectors are perpendicular	draft	Harry Flynn	09/03/2018 14:44
Vectors: Perpendicular vectors	draft	Lovkush Agarwal	11/03/2019 09:59

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Question statement

You are given the vectors $\boldsymbol{v} = \begin{pmatrix}\var{a} \\ \var{b} \\ \lambda \end{pmatrix}$ and $\boldsymbol{w} = \begin{pmatrix} \var{c} \\ \var{d} \\ \var{f} \end{pmatrix}$ .

Enter your answers to the following questions as fractions or integers, not decimals.

Give any introductory information the student needs.

			Name	Type	Generated Value

a	integer	6
c	integer	8
b	integer	-4
d	integer	6
g	integer	9
f	integer	10
s3	integer	1
s2	integer	-1
s1	integer	1
s5	integer	1
s4	integer	1
lambda	rational	-12/5
mu1	number	10
mu2	number	10
v	vector	vector(6,-4,-2.4)
w	vector	vector(8,6,10)
u	vector	vector(140,20,76)

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Name

Data type

Value

xxxxxxxxxx
 
s1*random(2..9)

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Description

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Generated value: `integer`

← Depends on:

→ Used by:

lambda
v

This variable doesn't seem to be used anywhere.

Parts

Part a) Gap-fill
1. Gap Number entry
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Part b) Gap-fill
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Find $\lambda \in \mathbb{R}$ such that $\boldsymbol{v}$ and $\boldsymbol{w}$ are orthogonal.

$\lambda =$ Unnamed gap

Advice

a)

$\boldsymbol{v}$ and $\boldsymbol{w}$ are perpendicular to one another when $\boldsymbol{v} \cdot \boldsymbol{w} = 0$ .

Now

$\begin{align} \boldsymbol{v} \cdot \boldsymbol{w} &= \simplify[]{{a}*{c}+{b}*{d}+lambda*{f}} \\ &= \simplify[std]{{f}*lambda+{a*c+b*d}} \end{align}$

Hence

$\boldsymbol{v} \cdot \boldsymbol{w} = 0 \implies \simplify[std]{{f}*lambda+{a*c+b*d}}=0 \implies \lambda = \simplify[std]{{-a*c-b*d}/{f}}$

b)

$\boldsymbol{v}$ is in the $xy$ plane when $\lambda=0$ .

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Harry's copy of Determine if vectors are perpendicular

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Taxonomy: mathcentre

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Harry Flynn 7 years, 1 month ago

Error in variable testing condition

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Warning

Generated value: `integer`

Parts

Gap-fill

a)

b)

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Error

Harry's copy of Determine if vectors are perpendicular

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

History

Comment

Checkpoint description

Harry Flynn 7 years, 1 month ago

Error in variable testing condition

Error

Warning

Generated value: integer

Parts

Gap-fill

a)

b)

Generated value: `integer`